SRC/zgeev.f(3)

NAME
SRC/zgeev.f

SYNOPSIS

  Functions/Subroutines
subroutine zgeev (jobvl, jobvr, n, a, lda, w, vl, ldvl, vr, ldvr, work, lwork, rwork, info)
ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Function/Subroutine Documentation

  subroutine zgeev (character jobvl, character jobvr, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( * ) w, complex*16, dimension( ldvl, * ) vl, integer ldvl, complex*16, dimension( ldvr, * ) vr, integer ldvr, complex*16, dimension( * ) work, integer lwork, double precision, dimension( * ) rwork, integer info)

ZGEEV computes the eigenvalues and, optionally, the left and/or right eigenvectors for GE matrices

Purpose:

    !>
    !> ZGEEV computes for an N-by-N complex nonsymmetric matrix A, the
    !> eigenvalues and, optionally, the left and/or right eigenvectors.
    !>
    !> The right eigenvector v(j) of A satisfies
    !>                  A * v(j) = lambda(j) * v(j)
    !> where lambda(j) is its eigenvalue.
    !> The left eigenvector u(j) of A satisfies
    !>               u(j)**H * A = lambda(j) * u(j)**H
    !> where u(j)**H denotes the conjugate transpose of u(j).
    !>
    !> The computed eigenvectors are normalized to have Euclidean norm
    !> equal to 1 and largest component real.
    !>

Parameters
    JOBVL

    !>          JOBVL is CHARACTER*1
    !>          = 'N': left eigenvectors of A are not computed;
    !>          = 'V': left eigenvectors of are computed.
    !>

    JOBVR

    !>          JOBVR is CHARACTER*1
    !>          = 'N': right eigenvectors of A are not computed;
    !>          = 'V': right eigenvectors of A are computed.
    !>

    N

    !>          N is INTEGER
    !>          The order of the matrix A. N >= 0.
    !>

    A

    !>          A is COMPLEX*16 array, dimension (LDA,N)
    !>          On entry, the N-by-N matrix A.
    !>          On exit, A has been overwritten.
    !>

    LDA

    !>          LDA is INTEGER
    !>          The leading dimension of the array A.  LDA >= max(1,N).
    !>

    W

    !>          W is COMPLEX*16 array, dimension (N)
    !>          W contains the computed eigenvalues.
    !>

    VL

    !>          VL is COMPLEX*16 array, dimension (LDVL,N)
    !>          If JOBVL = 'V', the left eigenvectors u(j) are stored one
    !>          after another in the columns of VL, in the same order
    !>          as their eigenvalues.
    !>          If JOBVL = 'N', VL is not referenced.
    !>          u(j) = VL(:,j), the j-th column of VL.
    !>

    LDVL

    !>          LDVL is INTEGER
    !>          The leading dimension of the array VL.  LDVL >= 1; if
    !>          JOBVL = 'V', LDVL >= N.
    !>

    VR

    !>          VR is COMPLEX*16 array, dimension (LDVR,N)
    !>          If JOBVR = 'V', the right eigenvectors v(j) are stored one
    !>          after another in the columns of VR, in the same order
    !>          as their eigenvalues.
    !>          If JOBVR = 'N', VR is not referenced.
    !>          v(j) = VR(:,j), the j-th column of VR.
    !>

    LDVR

    !>          LDVR is INTEGER
    !>          The leading dimension of the array VR.  LDVR >= 1; if
    !>          JOBVR = 'V', LDVR >= N.
    !>

    WORK

    !>          WORK is COMPLEX*16 array, dimension (MAX(1,LWORK))
    !>          On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
    !>

    LWORK

    !>          LWORK is INTEGER
    !>          The dimension of the array WORK.  LWORK >= max(1,2*N).
    !>          For good performance, LWORK must generally be larger.
    !>
    !>          If LWORK = -1, then a workspace query is assumed; the routine
    !>          only calculates the optimal size of the WORK array, returns
    !>          this value as the first entry of the WORK array, and no error
    !>          message related to LWORK is issued by XERBLA.
    !>

    RWORK

    !>          RWORK is DOUBLE PRECISION array, dimension (2*N)
    !>

    INFO

    !>          INFO is INTEGER
    !>          = 0:  successful exit
    !>          < 0:  if INFO = -i, the i-th argument had an illegal value.
    !>          > 0:  if INFO = i, the QR algorithm failed to compute all the
    !>                eigenvalues, and no eigenvectors have been computed;
    !>                elements i+1:N of W contain eigenvalues which have
    !>                converged.
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 178 of file zgeev.f.

Author

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